What is the equation of the line normal

Malik Dean

Malik Dean

Answered question

2022-04-09

What is the equation of the line normal to f(x)=1x2+2 at x=1?

Answer & Explanation

xcentricccrhb1

xcentricccrhb1

Beginner2022-04-10Added 12 answers

in simplifying the equation we get
(x2+2)12
We then apply the chain rule to get
-xx2+232
Then we substitute in 1 for x to find the gradient of the tangent at x=1
This results us getting -193, however we need the normal's gradient, not the tangent's. The normal times the tangent gives us -1, so therefore the gradient of the normal will be 93.
Now we know the gradient, we just need the co-ordinates which it runs through. We then sub x=1 back int the original equation to find the point which the normal will pass through. The y value, after subsitution is 13.
Therefore by substituting the numbers/values into the point gradient formula, we'll find the equation of the normal. The point gradient formula is
yy1=m(xx1)

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